Twisted Hessian curves

D.J. Bernstein; Chitchanok Chuengsatiansup; D. Kohel; T. Lange

doi:10.1007/978-3-319-22174-8_15

Twisted Hessian curves

D.J. Bernstein, Chitchanok Chuengsatiansup, D. Kohel, T. Lange

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

45 Citations (Scopus)

Abstract

This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, 8.77Mper bit for 256-bit variable-base single-scalar multiplication when curve parameters are chosen properly. This is faster than the best results known for cofactor 1, showing for the first time that points of order 3 are useful for performance and narrowing the gap to the speeds of curves with cofactor 4.

Original language	English
Title of host publication	Progress in Cryptology - LATINCRYPT 2015 (4th International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015)
Editors	K. Lauter, F. Rodríguez-Henríquez
Place of Publication	Cham
Publisher	Springer
Pages	269-294
Number of pages	26
ISBN (Print)	978-3-319-22173-1
DOIs	https://doi.org/10.1007/978-3-319-22174-8_15
Publication status	Published - 2015
Event	4th International Conference on Cryptology and Information Security in Latin America (LATINCRYPT 2015), August 23-26, 2015, Guadalajara, Mexico - Hotel De Mendoza, Guadalajara, Mexico Duration: 23 Aug 2015 → 26 Aug 2015

Publication series

Name	Lecture Notes in Computer Science
Volume	9230
ISSN (Print)	0302-9743

Conference

Conference	4th International Conference on Cryptology and Information Security in Latin America (LATINCRYPT 2015), August 23-26, 2015, Guadalajara, Mexico
Abbreviated title	LATINCRYPT 2015
Country/Territory	Mexico
City	Guadalajara
Period	23/08/15 → 26/08/15

Keywords

Complete addition laws
Double-base chains
Efficiency
Elliptic-curve arithmetic
Fast arithmetic
Hessian curves

Access to Document

10.1007/978-3-319-22174-8_15

https://eprint.iacr.org/2015/781

Cite this

Bernstein, D. J., Chuengsatiansup, C., Kohel, D., & Lange, T. (2015). Twisted Hessian curves. In K. Lauter, & F. Rodríguez-Henríquez (Eds.), Progress in Cryptology - LATINCRYPT 2015 (4th International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015) (pp. 269-294). (Lecture Notes in Computer Science; Vol. 9230). Springer. https://doi.org/10.1007/978-3-319-22174-8_15

Bernstein, D.J. ; Chuengsatiansup, Chitchanok ; Kohel, D. et al. / Twisted Hessian curves. Progress in Cryptology - LATINCRYPT 2015 (4th International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015). editor / K. Lauter ; F. Rodríguez-Henríquez. Cham : Springer, 2015. pp. 269-294 (Lecture Notes in Computer Science).

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author = "D.J. Bernstein and Chitchanok Chuengsatiansup and D. Kohel and T. Lange",

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Bernstein, DJ, Chuengsatiansup, C, Kohel, D & Lange, T 2015, Twisted Hessian curves. in K Lauter & F Rodríguez-Henríquez (eds), Progress in Cryptology - LATINCRYPT 2015 (4th International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015). Lecture Notes in Computer Science, vol. 9230, Springer, Cham, pp. 269-294, 4th International Conference on Cryptology and Information Security in Latin America (LATINCRYPT 2015), August 23-26, 2015, Guadalajara, Mexico, Guadalajara, Mexico, 23/08/15. https://doi.org/10.1007/978-3-319-22174-8_15

Twisted Hessian curves. / Bernstein, D.J.; Chuengsatiansup, Chitchanok; Kohel, D. et al.
Progress in Cryptology - LATINCRYPT 2015 (4th International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015). ed. / K. Lauter; F. Rodríguez-Henríquez. Cham: Springer, 2015. p. 269-294 (Lecture Notes in Computer Science; Vol. 9230).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Chuengsatiansup, Chitchanok

AU - Kohel, D.

AU - Lange, T.

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AB - This paper presents new speed records for arithmetic on a large family of elliptic curves with cofactor 3: specifically, 8.77Mper bit for 256-bit variable-base single-scalar multiplication when curve parameters are chosen properly. This is faster than the best results known for cofactor 1, showing for the first time that points of order 3 are useful for performance and narrowing the gap to the speeds of curves with cofactor 4.

KW - Complete addition laws

KW - Double-base chains

KW - Efficiency

KW - Elliptic-curve arithmetic

KW - Fast arithmetic

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Bernstein DJ, Chuengsatiansup C, Kohel D, Lange T. Twisted Hessian curves. In Lauter K, Rodríguez-Henríquez F, editors, Progress in Cryptology - LATINCRYPT 2015 (4th International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015). Cham: Springer. 2015. p. 269-294. (Lecture Notes in Computer Science). doi: 10.1007/978-3-319-22174-8_15

Twisted Hessian curves

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